Re: [EM] Voting Criteria 101, Four Criteria
OK, now on to the questions and responses on the other Criteria: From: Jameson Quinn [mailto:jameson.qu...@gmail.com] Sent: Sunday, June 16, 2013 10:36 PM Subject: Re: [EM] Voting Criteria 101, Four Criteria In which case it (I think) becomes even more obvious and pointless as a criteria (as any system that gave the victory to people who get less votes, however we are counting and measuring votes, would make no sense, I think.) Name: Participation Description: If a ballot is added which prefers A to B, the addition of the ballot must not change the winner from A to B Thoughts: This seems to make sense. If we do not require this, then we permit voting systems where trying to vote sincerely harms your interests. Also, any voting system that would fail Participation would be I think fragile and react in not always predictable ways - like IRV. SO this seems to me to be a solid requirement, that I can't imagine a system that failed this Criterion to have some other benefit so wonderful to make failing Participation worth overlooking - I cannot imagine it. You have fairly described the participation criterion. I would ask you to consider that this criterion focuses only on the direction of preference, not its strength; and so it is inevitably biased towards preferential systems, and dooms you to live within the limits set by Arrow's theorem. My two favorite systems - SODA voting and the as-yet-unnamed version of Bucklin - both fail this criterion, though I would argue they do so in relatively rare and minor ways, and both satisfy some weakened version of the criterion. I don't understand how a bias exists here. In every case I can currently imagine, if an election as it stands has A winning, and one more ballot is added which still prefers A to B, why should that ever cause the winner to change to B? Range/Score Voting: If A is winning, and the following ballot was added (A:90, B:89) A would still be winning. If IRV is being used and the following ballot is added (D first place, A second place, B third place) we wouldn't want B to suddenly be beating A. (Although in IRV I guess it could happen, but the point is that we wouldn't want it to, right?) This seems to be a serious issue. Whatever the voting method, if A is currently winning, and one more ballot gets added that happens to favor A with relation to B, how could it EVER be a good thing if B somehow becomes the winner through the addition of that ballot? I don't understand what bias has to do with the answer to that question? Also, how could Bucklin (as I understand it) *ever* fail this one? Because a ballot added that favors A to B under Bucklin would at minimum increase A by the same amount as B, possibly more, but would *never* increase B more than A, else the ballot could not be said to prefer A over B, right? OK, that's several questions. When would participation failure ever be a good thing? It wouldn't. But in voting theory, tradeoffs are common. A system which had other desirable features could fail a reasonable-sounding criterion, and if that failure is minor and/or rare enough, that could still be a good system. I'd argue that that's the case for Bucklin systems and the participation criterion. Though there are certainly many people here who would argue with me on that specific point, the fact is that choosing any system involves making tradeoffs. So, how does Bucklin fail participation? Imagine you had the following votes, giving candidates X and Y grades A-F 49: X:A Y:D 50: X:F Y:D The bloc of 50 voters is a majority, so they set the median. Or in Bucklin terms, Y reaches a majority at grade D, while X doesn't until grade F, so Y wins. Now add 2 votes with X:C Y:B. Now, X reaches a majority at grade B, while Y still doesn't until grade D. So now X wins, even though those votes favored the prior winner Y. I find this specific example implausible for multiple reasons, and think that actual cases of participation failure would be very rare. For instance, those last two voters could have voted X:F Y:B, and honestly expressed their preference without changing the result. OK, first of all, my brain does not seem to be able to handle letters on both sides of the colon (:), so with your permission, let me alter the typography of your example, hopefully functionally changing nothing: 49: X:1st Y:4th 50: X:5th Y:4th So if I understand this right, under Bucklin, we look at all 1st place votes (we need at least 50), and see if we have over half - we don't, so now we look at all 2nd, still no, all 3rd, still no, and only when we consider 4th place do we finally have enough votes for candidate Y to have enough to win. Now we add two votes: 2: X:3rd Y:2nd Now we repeat the process, not enough 1st place votes (we need at least 51), not enough 2nd place votes, and adding in 3rd place we now have 51, precisely what we need for X to win. OK I think I see what
Re: [EM] Voting Criteria 101, Four Criteria
On 06/16/2013 06:55 PM, Benjamin Grant wrote: With your kind indulgence, I would like some assistance in understanding and hopefully mastering the various voting criteria, so that I can more intelligently and accurately understanding the strengths and weaknesses of different voting systems. So, if it’s alright, I would like to explain what I understand about some of these voting criteria, a few at a time, perhaps, and perhaps the group would be willing to “check my math” as it were and see if I actually understand these, one by one? No problem :-) *Name*: *_Plurality_* *Description*: If A gets more “first preference” ballots than B, A must not lose to B. Be careful not to mistake Plurality, the criterion, from Plurality the method. Plurality, the criterion, says: If there are two candidates X and Y so that X has more first place votes than Y has any place votes, then Y shouldn't win. The Plurality criterion is only relevant when the voters may truncate their ballots. In it, there's an assumption that listed candidates are ranked higher than non-listed ones - a sort of Approval assumption, if you will. To show a concrete example: say a voter votes A first, B second, and leaves C off the ballot. Furthermore say nobody actually ranks C. Then C shouldn't win, because A has more first-place votes than C has any-place votes. *Name: _Majority_* *Description*: If one candidate is preferred by an absolute majority of voters, then that candidate must win. That's right. More specifically, if a candidate has a majority of the first place votes, he should win. There's also a setwise version (mutual majority) where the criterion goes if a group of candidates is listed ahead of candidates not in that group, on a majority of the ballots, then a candidate in that group should win. *Thoughts*: I might be missing something here, but this seems like a no-brainer. If over 50% of the voters want someone, they should get him, any other approach would seem to create minority rule? I guess a challenge to this criteria might be the following: using Range Voting, A gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from 80 out of 100 voters. A’s net is 5400, but B’s net is 6400, so B would win (everyone else got less). Does this fail the Majority Criterion, because A got a higher vote from over half, or does it fulfill Majority because B’s net was greater than A’s net?? There are usually two arguments against the Majority criterion from those that like cardinal methods. First, there's the pizza example: say three people are deciding on what piza to get. Two of them prefer pepperoni to everything else, but the last person absolutely can't have pepperoni. Then, the argument goes, it would be unreasonable and unflexible to pick the pepperoni pizza just because a majority wanted it. Second, there's the redistribution argument. Consider a public election where a candidate wants to confiscate everything a certain minority owns and then distribute the loot to the majority. If the electorate is simple enough, a majority might vote for that candidate, but the choice would not be a good one. Briefly: the argument against Majority is tyranny of majority. But ranked methods can't know whether any given election is a tyranny-of-majority one, and between erring in favor of the majority and in favor of a minority (which might not be a good minority at all), the former's better. Condorcet's jury theorem is one way of formalizing that. Rated methods could distinguish between tyranny-of-majority cases, were all the voters honest, but being subject to Gibbard and Satterthwaite just like ranked methods, they too can be gamed. There's usually a way for a majority to force a win if they absolutely want to, too[1]. *Name: _Participation_* *Description*: If a ballot is added which prefers A to B, the addition of the ballot must not change the winner from A to B *Thoughts*: This seems to make sense. If we do not require this, then we permit voting systems where trying to vote sincerely harms your interests. Also, any voting system that would fail Participation would be I think fragile and react in not always predictable ways – like IRV. SO this seems to me to be a solid requirement, that I can’t imagine a system that failed this Criterion to have some other benefit so wonderful to make failing Participation worth overlooking – I cannot imagine it. Welcome to the unintuitive world of voting methods :-) Arrow's theorem says you can't have unanimity (if everybody agrees that AB, B does not win), IIA (as you mention below) and non-dictatorship. Since one can't give up the latter two and have anything like a good ranked voting method, that means every method must fail IIA. The trade-off with Participation is similar. It is impossible, for instance, to have a method that passes both Participation and Condorcet, so one has to choose which is more important. Similarly,
Re: [EM] Voting Criteria 101, Four Criteria
-Original Message- From: Kristofer Munsterhjelm [mailto:km_el...@lavabit.com] Sent: Monday, June 17, 2013 12:09 PM Subject: Re: [EM] Voting Criteria 101, Four Criteria On 06/16/2013 06:55 PM, Benjamin Grant wrote: *Name*: *_Plurality_* *Description*: If A gets more first preference ballots than B, A must not lose to B. Be careful not to mistake Plurality, the criterion, from Plurality the method. Plurality, the criterion, says: If there are two candidates X and Y so that X has more first place votes than Y has any place votes, then Y shouldn't win. The Plurality criterion is only relevant when the voters may truncate their ballots. In it, there's an assumption that listed candidates are ranked higher than non-listed ones - a sort of Approval assumption, if you will. To show a concrete example: say a voter votes A first, B second, and leaves C off the ballot. Furthermore say nobody actually ranks C. Then C shouldn't win, because A has more first-place votes than C has any-place votes. OK, that makes sense. *Name: _Majority_* *Thoughts*: I might be missing something here, but this seems like a no-brainer. If over 50% of the voters want someone, they should get him, any other approach would seem to create minority rule? I guess a challenge to this criteria might be the following: using Range Voting, A gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from 80 out of 100 voters. A's net is 5400, but B's net is 6400, so B would win (everyone else got less). Does this fail the Majority Criterion, because A got a higher vote from over half, or does it fulfill Majority because B's net was greater than A's net?? There are usually two arguments against the Majority criterion from those that like cardinal methods. First, there's the pizza example: say three people are deciding on what piza to get. Two of them prefer pepperoni to everything else, but the last person absolutely can't have pepperoni. Then, the argument goes, it would be unreasonable and unflexible to pick the pepperoni pizza just because a majority wanted it. Second, there's the redistribution argument. Consider a public election where a candidate wants to confiscate everything a certain minority owns and then distribute the loot to the majority. If the electorate is simple enough, a majority might vote for that candidate, but the choice would not be a good one. Briefly: the argument against Majority is tyranny of majority. But ranked methods can't know whether any given election is a tyranny-of-majority one, and between erring in favor of the majority and in favor of a minority (which might not be a good minority at all), the former's better. Condorcet's jury theorem is one way of formalizing that. In my (limited) experience, every instance where there has been an allegation of tyranny of the majority, the reverse choice is something even worse, tyranny of the minority. While ultimately certain things, like human rights, shouldn't be a matter for voting at all, if something deserves a vote it probably deserves to serve the greatest good for the greatest number. To take your pizza analogy, if the two people *only* want pepperoni, it would be selfish of the third to expect the majority to bend to his desires. On the other hand, if the two people are already fine with *either* pepperoni or plain, then they will say so. Ultimately, the only time I find when people complain about the tyranny of the majority is when they are in a minority that doesn't want what the majority truly does - and that's just the downside of not being a dictator. So I guess I would say this - whenever you hear the phrase tyranny of the majority, you can probably indentify the speaker is *usually* someone who wants more power over the selection process than they ought to have. *Name: _Participation_* *Description*: If a ballot is added which prefers A to B, the addition of the ballot must not change the winner from A to B *Thoughts*: This seems to make sense. If we do not require this, then we permit voting systems where trying to vote sincerely harms your interests. Also, any voting system that would fail Participation would be I think fragile and react in not always predictable ways - like IRV. SO this seems to me to be a solid requirement, that I can't imagine a system that failed this Criterion to have some other benefit so wonderful to make failing Participation worth overlooking - I cannot imagine it. Welcome to the unintuitive world of voting methods :-) Arrow's theorem says you can't have unanimity (if everybody agrees that AB, B does not win), IIA (as you mention below) and non-dictatorship. Since one can't give up the latter two and have anything like a good ranked voting method, that means every method must fail IIA. Wow. I am just starting to get exposed to this stuff, but it is being a bitter pill to swallow
Re: [EM] Voting Criteria 101, Four Criteria
2013/6/17 Kristofer Munsterhjelm km_el...@lavabit.com On 06/16/2013 06:55 PM, Benjamin Grant wrote: With your kind indulgence, I would like some assistance in understanding and hopefully mastering the various voting criteria, so that I can more intelligently and accurately understanding the strengths and weaknesses of different voting systems. So, if it’s alright, I would like to explain what I understand about some of these voting criteria, a few at a time, perhaps, and perhaps the group would be willing to “check my math” as it were and see if I actually understand these, one by one? No problem :-) *Name*: *_Plurality_* *Description*: If A gets more “first preference” ballots than B, A must not lose to B. Be careful not to mistake Plurality, the criterion, from Plurality the method. Plurality, the criterion, says: If there are two candidates X and Y so that X has more first place votes than Y has any place votes, then Y shouldn't win. The Plurality criterion is only relevant when the voters may truncate their ballots. In it, there's an assumption that listed candidates are ranked higher than non-listed ones - a sort of Approval assumption, if you will. To show a concrete example: say a voter votes A first, B second, and leaves C off the ballot. Furthermore say nobody actually ranks C. Then C shouldn't win, because A has more first-place votes than C has any-place votes. Right. Kristofer's response here is better than mine was. *Name: _Majority_* *Description*: If one candidate is preferred by an absolute majority of voters, then that candidate must win. That's right. More specifically, if a candidate has a majority of the first place votes, he should win. There's also a setwise version (mutual majority) where the criterion goes if a group of candidates is listed ahead of candidates not in that group, on a majority of the ballots, then a candidate in that group should win. Kristofer gives the ranked version of Mutual Majority. The rated version is: If a group of candidates is listed at or above a certain rating, and those not in the group below that rating, on a majority of ballots, then a candidate in that group should win. This criterion, in at least one of its versions, is a prerequisite for IoC. I prefer the rated version, but those like Kristofer who are working within the Arrovian paradigm prefer the ranked one. (Note that the mere fact that the rated paradigm is newer than the Arrovian one does not necessarily make it better. Saari's ranked-symmetry paradigm is newer than Arrow's, and also in my opinion worse. So in this debate between people like me and people like Kristofer, there is no short cut to evaluating each side's arguments on their merits. I of course think I'm right, but Kristofer is a very smart guy, and you would be unwise to ignore his side.) *Thoughts*: I might be missing something here, but this seems like a no-brainer. If over 50% of the voters want someone, they should get him, any other approach would seem to create minority rule? I guess a challenge to this criteria might be the following: using Range Voting, A gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from 80 out of 100 voters. A’s net is 5400, but B’s net is 6400, so B would win (everyone else got less). Does this fail the Majority Criterion, because A got a higher vote from over half, or does it fulfill Majority because B’s net was greater than A’s net?? There are usually two arguments against the Majority criterion from those that like cardinal methods. First, there's the pizza example: say three people are deciding on what piza to get. Two of them prefer pepperoni to everything else, but the last person absolutely can't have pepperoni. Then, the argument goes, it would be unreasonable and unflexible to pick the pepperoni pizza just because a majority wanted it. Second, there's the redistribution argument. Consider a public election where a candidate wants to confiscate everything a certain minority owns and then distribute the loot to the majority. If the electorate is simple enough, a majority might vote for that candidate, but the choice would not be a good one. Briefly: the argument against Majority is tyranny of majority. But ranked methods can't know whether any given election is a tyranny-of-majority one, and between erring in favor of the majority and in favor of a minority (which might not be a good minority at all), the former's better. Condorcet's jury theorem is one way of formalizing that. Rated methods could distinguish between tyranny-of-majority cases, were all the voters honest, but being subject to Gibbard and Satterthwaite just like ranked methods, they too can be gamed. There's usually a way for a majority to force a win if they absolutely want to, too[1]. I agree 100% with what Kristofer has said here. *Name: _Participation_* *Description*: If a ballot is added which
[EM] Voting Criteria 101, Four Criteria
With your kind indulgence, I would like some assistance in understanding and hopefully mastering the various voting criteria, so that I can more intelligently and accurately understanding the strengths and weaknesses of different voting systems. So, if it's alright, I would like to explain what I understand about some of these voting criteria, a few at a time, perhaps, and perhaps the group would be willing to check my math as it were and see if I actually understand these, one by one? I'll start with what seem to be the simpler ones. (For what it's worth, my understanding comes from various websites that do not always agree with each other. Also, I have the fundamental belief that one cannot consider oneself to have mastered something until and unless one has the ability to understand it well enough to explain it to someone else - which is what I will try to do below, re-explain these criteria as a test to see if I really get them.) Name: Plurality Description: If A gets more first preference ballots than B, A must not lose to B. Thoughts: If I understand this correctly, this is not a critical criteria to my way of thinking. Consider an election with 10 candidates. A gets 13% of the first place votes, more than any other single candidate. And yet B gets 8% of the first place votes, and 46% of the second place votes. It seems obvious to me that B ought to win. And yet, in this circumstance, this violates the above Plurality Criterion. Therefor is seems to be that the Plurality Criterion is not useful, to my way of thinking. Name: Majority Description: If one candidate is preferred by an absolute majority of voters, then that candidate must win. Thoughts: I might be missing something here, but this seems like a no-brainer. If over 50% of the voters want someone, they should get him, any other approach would seem to create minority rule? I guess a challenge to this criteria might be the following: using Range Voting, A gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from 80 out of 100 voters. A's net is 5400, but B's net is 6400, so B would win (everyone else got less). Does this fail the Majority Criterion, because A got a higher vote from over half, or does it fulfill Majority because B's net was greater than A's net?? Name: Participation Description: If a ballot is added which prefers A to B, the addition of the ballot must not change the winner from A to B Thoughts: This seems to make sense. If we do not require this, then we permit voting systems where trying to vote sincerely harms your interests. Also, any voting system that would fail Participation would be I think fragile and react in not always predictable ways - like IRV. SO this seems to me to be a solid requirement, that I can't imagine a system that failed this Criterion to have some other benefit so wonderful to make failing Participation worth overlooking - I cannot imagine it. Name: Independence of Irrelevant Alternatives (IIA) Description: Adding a new candidate B to an election that previously A would have won must not cause anyone apart from A or B to win. That is, If A would have won before B was added to the ballot, C must not win now. Thoughts: This also seems fairly non-controversial. This I think is the repudiation of the spoiler effect - that just because Nader enters the race shouldn't disadvantage the candidate that would have won before that happened. This would seem (to me) to also be a good Criterion to hold to in order to encourage more than just two Candidates/Parties always dominating the scene. I wonder what the downside would be to strongly embracing this criteria? Question: It seems to me that another criterion I have heard of - Independence of Clones(IoC) - is a subset of IIA, that if a system satisfies IIA, it would have to satisfy the Independence of Clones criterion as well - is that correct? If not, what system what satisfy IoC but *not* satisfy IIA? Question: it seems like the two above criteria - Participation and IIA - would be related. Is it possible to fail one and not the other? Or does either wind up mandate the other - for example, a system with IIA must also fulfill Participation, or vice versa? So let me stop there for now - I know there are other Criteria, but let me pause so you guys can tell me what I am getting right and what I am getting wrong. Thanks. -Benn Grant eFix Computer Consulting mailto:b...@4efix.com b...@4efix.com 603.283.6601 Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Voting Criteria 101, Four Criteria
2013/6/16 Benjamin Grant b...@4efix.com ...I would like to explain what I understand about some of these voting criteria, a few at a time... Thanks for doing this, and again, welcome. *Name*: *Plurality* *Description*: If A gets more “first preference” ballots than B, A must not lose to B. *Thoughts*: If I understand this correctly, this is not a critical criteria to my way of thinking. Consider an election with 10 candidates. A gets 13% of the first place votes, more than any other single candidate. And yet B gets 8% of the first place votes, and 46% of the second place votes. It seems obvious to me that B “ought” to win. And yet, in this circumstance, this violates the above Plurality Criterion. Therefor is seems to be that the Plurality Criterion is not useful, to my way of thinking. I think that most here would agree with what you've said. ** ** *Name: Majority* *Description*: If one candidate is preferred by an absolute majority of voters, then that candidate must win. Presumably, by preferred, you mean preferred over all others. This definition is actually a bit controversial. I'll explain, but I have to go back a bit. Note that all that follows is my personal opinion; it's far too opinionated to pass muster at Wikipedia, and though I suspect that some here would agree with most of it, I'm also sure that others will chime in to debate me on some points. The modern science of voting theory begins with Kenneth Arrow in the 1950s. I happen to be reading Kuhn (*The Structure of Scientific Revolutions*) at the moment, so I'll use his terms. Before Arrow, the study of single-winner voting systems was disorganized and unscientific; though figures such as Maurice Duverger and Duncan Black had important insights into the incentives of plurality on parties and voters, they could offer little guidance as to how to improve the situation. Arrow offered the first paradigm for the field. The Arrovian paradigm is essentially preferential, and it tends to lead toward Condorcet systems as being best. From its very beginning, Arrow's own theorem marked sharp limits to how far you could go within his paradigm. Nonetheless, as Kuhn quotes from Bacon, error leads to truth more quickly than confusion; that is, even a flawed paradigm is immensely more productive than prescientific disorganization. For instance, the important Gibbard-Satterthwaite theorem on strategy followed close on the heels of Arrow's result. Since Arrow, there have been other paradigms advanced. Around 1980, Steven Brams suggested Approval Voting, a simple idea which prior to that had been used but never theorized. This was clearly a step out of the Arrovian paradigm, but it didn't quite yet offer an alternative basis for further research and refinement. Donald Saari then reacted against approval by advancing a paradigm based on ordinal ballots and mathematical symmetry (and thus, Borda voting); in my opinion, his willful ignorance of strategic issues makes his way of thinking ultimately counterproductive, though some of the tools he created are useful. So the first person to offer a truly fertile alternative to the Arrovian paradigm was, in my opinion, Warren Smith (active on this list), with his 1999 paper on Range Voting. This system, now mostly called Score Voting, goes beyond approval to allow fractional ratings. The division between Arrovian, preferential systems, and Score-like systems has been expressed using multiple terms: ranked versus rated (with rated systems sometimes further subdivided into rated or graded); ordinal versus cardinal; preferential versus ???; and my own favorite terms, comparative versus evaluative. Since Smith, there has also been work in yet another paradigm, that of delegation. The DemoEx party in Sweden, the study of Asset voting, liquid democracy, delegable proxy, delegated yes-no (DYN), the revival of interest in Dodgson's 19th-century proposal for delegated proportional representation, and most recently my own proposal Simple Optionally-delegated Approval (SODA) all lie in this line of inquiry. Still, as always, there are some who continue to mine the vein of the old Arrovian paradigm, and it can't be said that that vein is entirely played out. The new paradigms also remain much less well-established academically; for instance, Smith's seminal paper has never been published in a peer-reviewed journal. So all of that history is a backdrop for the debate over how to apply the definitions of such criteria as Majority and Mutual Majority to evaluative systems. Your definition of Majority uses the word preferred, which inevitably biases it towards ranked thinking. An advocate for evaluative systems, like myself, would argue that it would be better to say voted as favorably as possible. This distinction makes no difference at all for a comparative system — a candidate who is preferred over all others is, by definition, at the very top of any purely comparative ballot
Re: [EM] Voting Criteria 101, Four Criteria
, and A would win, but then B enters the race, I can get A still winning. I can get B leaping ahead somehow and winning. What I cannot understand is how a candidate that A was beating before B's entry, somehow A now loses to. At least I cannot understand how any system that fails this criteria could still be worth considering - how the outcome of A beating C *until* B enters the race, after which C wins, is desirable. Is there some example that explain how this turn of events could be somehow fair or sensible? Independence of Clones: since you are saying that IoC is not equivalent with IIA, I will take up IoC independently along the way in a later set of criteria. I still am curious about this question: Question: it seems like the two above criteria - Participation and IIA - would be related. Is it possible to fail one and not the other? Or does either wind up mandating the other - for example, a system with IIA must also fulfill Participation, or vice versa? Thanks for your time and help - and please, anyone who wants to chime in, please do so, this is not just a conversation between myself and Jameson, but between me and the community her. Thanks! :) -Benn Grant eFix Computer Consulting mailto:b...@4efix.com b...@4efix.com 603.283.6601 From: Jameson Quinn [mailto:jameson.qu...@gmail.com] Sent: Sunday, June 16, 2013 4:44 PM To: Benjamin Grant Cc: election-methods@lists.electorama.com Subject: Re: [EM] Voting Criteria 101, Four Criteria 2013/6/16 Benjamin Grant b...@4efix.com mailto:b...@4efix.com ...I would like to explain what I understand about some of these voting criteria, a few at a time... Thanks for doing this, and again, welcome. Name: Plurality Description: If A gets more first preference ballots than B, A must not lose to B. Thoughts: If I understand this correctly, this is not a critical criteria to my way of thinking. Consider an election with 10 candidates. A gets 13% of the first place votes, more than any other single candidate. And yet B gets 8% of the first place votes, and 46% of the second place votes. It seems obvious to me that B ought to win. And yet, in this circumstance, this violates the above Plurality Criterion. Therefor is seems to be that the Plurality Criterion is not useful, to my way of thinking. I think that most here would agree with what you've said. Name: Majority Description: If one candidate is preferred by an absolute majority of voters, then that candidate must win. Presumably, by preferred, you mean preferred over all others. This definition is actually a bit controversial. I'll explain, but I have to go back a bit. Note that all that follows is my personal opinion; it's far too opinionated to pass muster at Wikipedia, and though I suspect that some here would agree with most of it, I'm also sure that others will chime in to debate me on some points. The modern science of voting theory begins with Kenneth Arrow in the 1950s. I happen to be reading Kuhn (The Structure of Scientific Revolutions) at the moment, so I'll use his terms. Before Arrow, the study of single-winner voting systems was disorganized and unscientific; though figures such as Maurice Duverger and Duncan Black had important insights into the incentives of plurality on parties and voters, they could offer little guidance as to how to improve the situation. Arrow offered the first paradigm for the field. The Arrovian paradigm is essentially preferential, and it tends to lead toward Condorcet systems as being best. From its very beginning, Arrow's own theorem marked sharp limits to how far you could go within his paradigm. Nonetheless, as Kuhn quotes from Bacon, error leads to truth more quickly than confusion; that is, even a flawed paradigm is immensely more productive than prescientific disorganization. For instance, the important Gibbard-Satterthwaite theorem on strategy followed close on the heels of Arrow's result. Since Arrow, there have been other paradigms advanced. Around 1980, Steven Brams suggested Approval Voting, a simple idea which prior to that had been used but never theorized. This was clearly a step out of the Arrovian paradigm, but it didn't quite yet offer an alternative basis for further research and refinement. Donald Saari then reacted against approval by advancing a paradigm based on ordinal ballots and mathematical symmetry (and thus, Borda voting); in my opinion, his willful ignorance of strategic issues makes his way of thinking ultimately counterproductive, though some of the tools he created are useful. So the first person to offer a truly fertile alternative to the Arrovian paradigm was, in my opinion, Warren Smith (active on this list), with his 1999 paper on Range Voting. This system, now mostly called Score Voting, goes beyond approval to allow fractional ratings. The division between Arrovian, preferential systems, and Score-like systems has been expressed using multiple terms: ranked
